with total expenses of $6,390 and take-home pay of $7,450, how much money is left for savings?

Kye
2020-12-25
Answered

with total expenses of $6,390 and take-home pay of $7,450, how much money is left for savings?

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au4gsf

Answered 2020-12-26
Author has **95** answers

The amount left over for savings is the take-home pay minus the total expenses.

If the take-home pay is $7,450 and the total expenses are $6,390, then the amount of money left over for savings is $7,450−$6,390=$1,060

If the take-home pay is $7,450 and the total expenses are $6,390, then the amount of money left over for savings is $7,450−$6,390=$1,060

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${\mathrm{\Delta}}_{n-1}:=\{x\in {R}^{n}:{x}_{1}+{x}_{2}+....{x}_{n}=1,{x}_{1},{x}_{2},....{x}_{n}\ge 0\}$

and

$a\in {R}^{n}$

Let

$z:={P}_{{\mathrm{\Delta}}_{n-1}}(a)$

be the projection of point a onto ${\mathrm{\Delta}}_{n-1}$. Show that $z$ satisfies the system of inequalities

$z-y=a-\mu \mathbf{\text{e}},z\ge 0,y\ge 0,{z}^{T}y=0$

where $\mathbf{\text{e}}$ is the vector of all ones. $y,z\in {R}^{n},\mu \in R$. One can use obtuse angle condition of the projection theorem over the convex set along with Farkas Lemma.

I don't know how to approach this problem.

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